Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter

2024/04/24 by Baoli Hao, Ulisses Braga-Neto, Hao, Baoli +7 · 1 citation
Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2404.16189

openalex publication_date 2024/04/24 · openalex created_date 2024/04/27 · openalex updated_date 2026/07/30

Abstract

Training Physics-Informed Neural Networks (PINNs) on stiff time-dependent PDEs remains highly unstable. Through rigorous ablation studies, we identify a surprisingly critical factor: the enforcement of initial conditions. We present the first systematic ablation of two core strategies, hard initial-condition constraints and adaptive loss weighting. Across challenging benchmarks (sharp transitions, higher-order derivatives, coupled systems, and high frequency modes), we find that exact enforcement of initial conditions (ICs) is not optional but essential. Our study demonstrates that stability and efficiency in PINN training fundamentally depend on ICs, paving the way toward more reliable PINN solvers in stiff regimes.

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